Apparatus and method for measuring parameters of a mixture having solid particles suspended in a fluid flowing in a pipe

ABSTRACT

An apparatus  10  and method is provided that includes a spatial array of unsteady pressure sensors  15 - 18  placed at predetermined axial locations x 1 -x N  disposed axially along a pipe  14  for measuring at least one parameter of a solid particle/fluid mixture  12  flowing in the pipe  14 . The pressure sensors  15 - 18  provide acoustic pressure signals P 1 (t)-P N (t) to a signal processing unit  30  which determines the speed of sound a mix (ω) of the particle/fluid mixture  12  in the pipe  14  using acoustic spatial array signal processing techniques. The primary parameters to be measured include fluid/particle concentration, fluid/particle mixture volumetric flow, and particle size. Frequency based sound speed is determined utilizing a dispersion model to determine the parameters of interest. the calculating the at least one parameter uses an acoustic pressure to calculate.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation in part of U.S. patent applicationSer. No. 10/376,427, filed on Feb. 26, 2003, now U.S. Pat. No.7,032,432, which claimed the benefit of U.S. Provisional Application No.60/359,785, filed Feb. 26, 2002; and which is a continuation in part ofU.S. patent application Ser. No. 10/349,716, filed Jan. 23, 2003, whichclaims the benefit of U.S. Provisional Application No. 60/351,232, filedJan. 23, 2002; U.S. Provisional Application No. 60/359,785, filed Feb.26, 2002; U.S. Provisional Application No. 60/375,847, filed Apr. 24,2002; U.S. Provisional Application No. 60/425,436, filed Nov. 12, 2002;and U.S. Provisional Application No. 60/426,724, filed Nov. 15, 2002;all of which are incorporated herein by reference in their entirety.

TECHNICAL FIELD

This invention relates to an apparatus for measuring the flow passingwithin a pipe, and more particularly to an apparatus and method formeasuring the speed of sound propagating in the flow, having particlessuspended within a continuous fluid, to determine parameters, such asparticle/fluid ratio, particle size and volumetric flow rate of the flowin pipes using acoustic dynamic pressures.

BACKGROUND ART

This invention provides a method to measure parameters of afluid/particle mixture in a pipe that can be used in many applications,such as in chemical, pharmaceutical, petroleum and power generationindustries. In particular, the invention provides a method to measurepulverized coal and air mixtures used in pulverized fuel deliverysystems in place in a large percentage of coal fired boilers used in thepower generation industry.

Currently, well over 50% of the electricity in the US is generated withcoal. While coal is considered a cost effective, abundant resource inthe US, the use of coal has been restricted due in large part toenvironmental concerns. To mitigate this impact, the US Department ofEnergy and the Power Generation industry have large programs designed todevelop technology to reduce the environment effects of burning coal.These Clean Coal Initiatives include technology designed to developimprovements in the combustion process to improve efficiency whilereducing pollutants such as unburned carbon, ash, and nitrous oxide(NOx).

The ability to measure the flow rate and composition of the air/coalmixture within the coal pipes is an important aspect of any system orstrategy designed to optimize the performance of the PF delivery system.The industry recognizes this and therefore has been developing a widevariety of technologies to perform this measurement. These include probebased and sampling devices, as well as real time meters based on a widevariety of technologies including electrostatic charges, microwaves, andultrasonic.

SUMMARY OF THE INVENTION

Objects of the present invention include providing a system formeasuring the speed of sound propagating through a particle/fluidmixture in pipes in industrial boiler systems and related processes,such as coal fired boiler systems, to determine particular parameters ofthe mixture.

According to the present invention, an apparatus for measuring at leastone parameter of a particle/fluid mixture in a pipe includes a spatialarray of at least two pressure sensors, disposed at different axiallocations along the pipe. Each of the pressure sensors measures anunsteady pressure within the pipe at a corresponding axial location.Each of said sensors provides a pressure signal indicative of theunsteady pressure within the pipe at said axial location of acorresponding one of said sensors. A signal processors responsive tosaid pressure signals, provides a signal indicative of the at least oneparameter of the mixture in the pipe.

According to the present invention, a method for measuring at least oneparameter of a particle/fluid mixture in a pipe includes measuringunsteady pressures within the pipe at at least two predetermined axialmeasurement locations along the pipe to provide a pressure signalindicative of the unsteady pressure within the pipe at each of the atleast two predetermined axial measurement locations. Further the methodincludes calculating the at least one parameter of the particle/fluidmixture in the pipe using the unsteady pressure measured at the axialmeasurement locations.

The foregoing and other objects, features and advantages of the presentinvention will become more apparent in light of the following detaileddescription of exemplary embodiments thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a flow meter for measuring the speed ofsound of the fluid/particle mixture flowing with a pipe, in accordancewith the present invention.

FIG. 2 is a schematic diagram of a pulverized fuel (PF)/air mixtureparameter measurement system within a coal fired boiler system, inaccordance with the present invention.

FIG. 3 is a magnified photograph showing particle size of coal typicalof the system shown in FIG. 2.

FIG. 4 is a plot of the speed of sound of a mixture versus the frequencyin air/coal mass flow ratio, in accordance with the present invention.

FIG. 5 is a plot of actual data and a model of the speed of sound as afunction of frequency for air/coal mixtures, in accordance with thepresent invention.

FIG. 6 is a plot showing the standard deviation of sound speed versusfrequency for various arrays of a PF/air mixture parameter measurementsystem, in accordance with the present invention.

FIG. 7 is a plot of sound speed as a function of frequency for air/coalmixtures with fixed particle size (50 mm) and varying air-to-fuel massratio in accordance with the present invention.

FIG. 8 is a plot of sound speed as a function of frequency for air/coalmixtures with varying particle size where the air-to-fuel mass ratio isequal to 1.8 in accordance with the present invention.

FIG. 9 is a plot of sound speed as function of air/coal ratio inaccordance with the present invention.

FIG. 10 is a flow diagram of an optimization procedure employed todetermine air-to-fuel ratio and particle size from analytical model andexperimentally determined dispersive speed of sound data in accordancewith the present invention.

FIG. 11 is a plot of the results of the optimization procedure of FIG.10 applied to data recorded from an array of sensors listening to flowin a six inch circular duct, 50 μm particle size, 100 ft/sec air flowrate with an air-to-fuel ratio of 1.8.

FIG. 12 is a plot of the results of the optimization procedure of FIG.10 applied to a series of data sets with varying air-to-fuel ratio.

FIG. 13 is a kω plot of data processed from an array of pressure sensorsuse to measure the speed of sound of a coal/air mixture flowing in apipe, in accordance with the present invention.

FIG. 14 is a side elevational view of a plurality of pressure sensors,having PVDF, clamped to the outer surface of the pipe, in accordancewith the present invention.

FIG. 15 is a partial perspective view of one of the pressure sensors ofFIG. 14.

BEST MODE FOR CARRYING OUT THE INVENTION

Referring to FIG. 1, a flow meter 10 embodying the present invention isprovided that measures a number of parameters/characteristics of amixture 12 of solid particles suspended within a continuous fluidflowing within a pipe or conduit 14, wherein a fluid is defined as aliquid and/or a gas. The flow meter may be configured and programmed tomeasure the speed of sound propagating through the mixture. The flowmeter can measure at least one of the following parameters of themixture flow 12: the fluid/particle concentration (volumetric phasefraction), the volumetric flow rate, the size of the solid particles,the mass flow of the mixture and the velocity of the mixture. Todetermine any one of these parameters, the flow meter 10 measures theunsteady pressures created by the speed of sound (SOS) propagatingthrough the mixture flowing in the pipe 14, which will be described ingreater detail hereinafter.

The solid particles of the mixture 12 may be of any size, shape andmaterial. For example, the particles may be small in size as in the formof a powder, in a granular form, or greater in size. The flow meter 10can be used in any application that carries solid particles suspended ina fluid through a pipe, such as in chemical, pharmaceutical, petroleumand power generation applications. For example, the present invention iswell suited to measure the parameters (e.g. air/coal ratio, particlesize) for power generation systems that use pulverized coal to fire thefurnace a steam boiler system.

As one example, the present invention will be discussed in the contextof a Pulverized Fuel (PF) delivery system for power generation, but onewill appreciate that the flow meter can be applied to any number ofother applications, as discussed hereinbefore. A representative PFdelivery system 1 is shown in a coal fired boiler system 2 in FIG. 2.The coal is pulverized in a mill 3 and entrained in air produced by manymeans, such as a fan 4 to transport the PP/air mixture via pipes 12 fordelivery to the furnace 6. Typical furnaces can have greater than fiftycoal pipes, each twelve to 20 inches in diameter. Typically, a largeutility boiler >300 Mw, can have four to eleven pulverizing millsfeeding the furnace. The ability of the PF delivery system to deliverthe proper amount of fuel and air to the furnace through these multiplecoal pipes, both collectively and individually, has a strong influenceon the performance and emissions from the coal fired boiler.

As is known, non-uniformities in the PF delivery system 1 can result invariation of the fuel to air ratios, causing hot spots, regions of highNOx generation, and unburned fuel. The connection between performance ofa PF fuel delivery system 1 and boiler system 2 is well recognized. Theflow meter 10 embodying the present invention is capable of measuringthe fuel to air ratio and particle size of the pulverized coal providedto the furnace to thereby provide feedback to the operator to providemore efficient combustion of the coal.

As described hereinbefore, the flow meter 10, of the present inventionmay be configured and programmed to measure and process the detectedunsteady pressures P_(l)(t)-P_(N)(t) created by acoustic wavespropagating through the mixture to determine parameters of tbe mixtureflow 12. One such flow meter 10 is shown in FIG. 1 that measures thespeed of sound (SOS) of one-dimensional sound waves propagating throughthe fluid/particle mixture to determine the composition the mixture,namely the liquid/particle ratio of the mixture. The flow meter is alsocapable of determining the average size of the particles, velocity ofthe mixture, and the volumetric flow rate of the mixture. It is knownthat sound propagates through various mediums at various speeds in suchfields as SONAR and RADAR fields. The speed of sound of a mixture withina pipe 14 may be determined using a number of known techniques, such asthose set forth in U.S. Pat. No. 6,354,147, entitled “Fluid ParameterMeasurement in Pipes Using Acoustic Pressures”, issued Mar. 12, 2002,and U.S. patent application Ser. No. 10/007,749, entitled “FluidParameter Measurement in Pipes Using Acoustic Pressures”, filed Nov. 7,2001, now U.S. Pat. No. 6,732,575, each of which are incorporated hereinby reference. The present invention utilizes at least one flow meter 10to determine various parameters of the liquid/particle mixture, whereinone of the parameters is the speed at which sound travels within themixture pipe system as will be more fully described herein below.

In accordance with the present invention, the speed of sound propagatingthrough the mixture 12 is measured by passively listening to the flowwith an array of unsteady pressure sensors to determine the speed atwhich one-dimensional compression waves propagate through theliquid/particle mixture contained within the pipe 14.

As shown in FIG. 1, the flow meter 10 has an array of at least threeacoustic pressure sensors 15,16,17, located at three locations x₁,x₂,x₃axially along the pipe 14. One will appreciate that the sensor array mayinclude more than three pressure sensors as depicted by pressure sensor18 at location x_(N). The pressure generated by the acoustic waves maybe measured through holes in the pipe 14 reported external pressuresensors 15-18 or by other techniques discussed hereinafter. The pressuresensors 15-18 provide pressure time-varying signalsP₁(t),P₂(t),P₃(t),P_(N)(t) on lines 20,21,22,23 to a signal processingunit 30 to known Fast Fourier Transform (FFT) logics 26,27,28, 29,respectively. The FFT logics 26-29 calculate the Fourier transform ofthe time-based input signals P₁(t)-P_(N)(t) and provide complexfrequency domain (or frequency based) signals P₁(ω),P₂(ω),P₃(ω),P_(N)(ω)on lines 32,33,34,35 indicative of the frequency content of the inputsignals. Instead of FFT's, any other technique for obtaining thefrequency domain characteristics of the signals P_(l)(t)-P_(N)(t), maybe used. For example, the cross-spectral density and the power spectraldensity may be used to form a frequency domain transfer functions (orfrequency response or ratios) discussed hereinafter.

The frequency signals P_(l)(ω)-P_(N)(ω) are fed to a_(mix)-MxCalculation Logic 38 which provides a signal to line 40 indicative ofthe speed of sound propagating through the mixture a_(mix)(ω), which isa function frequency (discussed more hereinafter). The a_(mix)(ω) signalis provided to map (or equation) logic 42, which converts a_(mix)(ω) toa percent composition of the PF/air mixture and provides a % Comp signalto line 44 indicative thereof (as discussed hereinafter). Also, if theMach number Mx(ω) is not negligible and is desired, the calculationlogic 38 may also provide a signal Mx(ω) to line 46 indicative of theMach number Mx(ω) which is a function of frequency.

For circular ducts or pipes 14 as shown in FIG. 1, only plane wavespropagate for frequencies below the cut-on frequency (ref Acoustics ofDucts and Mufflers, M.J. Munjal, John Wiley & Sons, New York, 1987):

$f < {\frac{1.84}{\pi\; D}a}$

For a mixture with a sound speed of 500 m/sec in an eighteen inch pipe,the cut-off frequency is approximately 600 Hz. Thus, for this example,only one-dimensional acoustic waves propagate below 600 Hz. It isimportant to note that one-dimensionai waves can still propagate abovethis frequency, but higher order modes may or may not be present.

More specifically, for planar one-dimensional acoustic waves in ahomogenous mixture, it is known that the acoustic pressure field P(x,t)at a location x along a pipe, where the wavelength λ of the acousticwaves to be measured is long compared to the diameter d of the pipe 14(i.e., λ/d>>1), may be expressed as a superposition of a right travelingwave and a left traveling wave, as follows:P(x,t)=(Ae ^(−ik) ^(r) ^(x) +Be ^(+ik) ^(l) ^(x))e ^(iωt)  Eq. 1where A,B are the frequency-based complex amplitudes of the right andleft traveling waves, respectively, x is the pressure measurementlocation along a pipe, ω is frequency (in rad/sec, where ω=2πf), andk_(r),k_(l) are wave numbers for the right and left travelling waves,respectively, which are defined as:

$\begin{matrix}\begin{matrix}{{k_{r} \equiv {\left( \frac{\omega}{a_{mix}(\omega)} \right)\frac{1}{1 + {M_{x}(\omega)}}\mspace{14mu}{and}}}\mspace{14mu}} \\{{k_{l} \equiv {\left( \frac{\omega}{a_{mix}(\omega)} \right)\frac{1}{1 - {M_{x}(\omega)}}}}\mspace{65mu}}\end{matrix} & {{Eq}.\mspace{14mu} 2}\end{matrix}$where a_(mix)(ω) is the speed of sound of the mixture in the pipe, ω isfrequency (in rad/sec), and M_(x)(ω) is the axial Mach number of theflow of the mixture within the pipe, where:

$\begin{matrix}{{M_{x}(\omega)} \equiv \frac{V_{mix}}{a_{mix}(\omega)}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

where Vmix is the axial velocity of the mixture. For non-homogenousmixtures, the axial Mach number represents the average velocity of themixture and the low frequency acoustic field description remainssubstantially unaltered.

The frequency domain representation P(x,ω) of the time-based acousticpressure field P(x,t) Within a pipe, is the coefficient of the e^(iωt)term of Eq. 1, as follows:P(x,ω)=Ae ^(−ik) ^(r) ^(x) +Be ^(+ik) ^(l) ^(x)  Eq. 4

Referring to FIG. 1, we have found that using Eq. 4 for P(x,ω) at threeaxially distributed pressure measurement locations x₁,x₂,x₃ along thepipe 14 leads to an equation for a_(mix) as a function of the ratio offrequency based pressure measurements, which allows the coefficients A,Bto be eliminated. For optimal results, A and B are substantiallyconstant over the measurement time and substantially no sound (oracoustic energy) is created or destroyed in the measurement section. Theacoustic excitation enters the test section only through the ends of thetest section 50 and, thus, the speed of sound within the test section 50can be measured independent of the acoustic environment outside of thetest section. In particular, the frequency domain pressure measurementsP₁(ω),P₂(ω),P₃(ω) at the three locations x₁,x₂,x₃, respectively alongthe pipe 14 using Eq. 1 for right and left traveling wvaes as follows:P ₁(ω)=P(x=x ₁,ω)=Ae ^(−ik) ^(r) ^(x) ¹ +Be ^(+ik) ^(I) ^(x) ¹   Eq. 5P ₂(ω)=P(x=x ₂,ω)=Ae ^(ik) ^(r) ^(x) ² +Be ^(+ik) ^(l) ^(x) ²   Eq. 6P ₃(ω)=P(x=x ₃,ω)=Ae ^(−ik) ^(r) ^(x) ³ +Be ^(+ik) ^(I) ^(x) ³   Eq. 7where, for a given frequency, A and B are arbitrary constants describingthe acoustic field between the sensors 15,16,17. Forming the ratio ofP₁(ω)/P₂(ω) from Eqns. 6, 7, and solving for B/A, gives the followingexpression:

$\begin{matrix}{{R \equiv \frac{B}{A}} = \frac{{\mathbb{e}}^{{- {\mathbb{i}}}\; k_{r}x_{1}} - {\left\lbrack \frac{P_{1}(\omega)}{P_{2}(\omega)} \right\rbrack{\mathbb{e}}^{{- {\mathbb{i}}}\; k_{r}x_{2}}}}{{\left\lbrack \frac{P_{1}(\omega)}{P_{2}(\omega)} \right\rbrack{\mathbb{e}}^{{- {\mathbb{i}}}\; k_{l}x_{2}}} - {\mathbb{e}}^{{- {\mathbb{i}}}\; k_{l}x_{1}}}} & {{Eq}.\mspace{14mu} 8}\end{matrix}$where R is defined as the reflection coefficient.

Forming the ratio of P₁(ω)/P₃(ω) from Eqs. 5 and 7 and solving for zerogives:

$\begin{matrix}{{\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\; k_{r}x_{1}} + {Re}^{{\mathbb{i}}\; k_{l}x_{1}}}{{\mathbb{e}}^{{- {\mathbb{i}}}\; k_{r}x_{3}} + {Re}^{{\mathbb{i}}\; k_{l}x_{3}}} - \left\lbrack \frac{P_{1}(\omega)}{P_{2}(\omega)} \right\rbrack} = 0} & {{Eq}.\mspace{14mu} 9}\end{matrix}$where R=B/A is defined by Eq. 8 and kr and kl are related to a_(mix) asdefined by Eq. 2. Eq. 9 may be solved numerically, for example, bydefining an “error” or residual term as the magnitude of the left sideof Eq. 9, and iterating to minimize the error term.

$\begin{matrix}{{{mag}\left\lbrack {\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\; k_{r}x_{1}} + {Re}^{{\mathbb{i}}\; k_{l}x_{1}}}{{\mathbb{e}}^{{- {\mathbb{i}}}\; k_{r}x_{3}} + {Re}^{{\mathbb{i}}\; k_{l}x_{3}}} - \left\lbrack \frac{P_{1}(\omega)}{P_{2}(\omega)} \right\rbrack} \right\rbrack} \equiv {Error}} & {{Eq}.\mspace{14mu} 10}\end{matrix}$

The data from the array of sensors may be processed in any domain,including the frequency/spatial domain, the temporal/spatial domain, thetemporal/wave-number domain or the wave-number/frequency (k−ω) domain.As such, any known array processing technique in any of these or otherrelated domains may be used if desired.

Also, some or all of the functions within the signal processing unit 30may be implemented in software (using a microprocessor or computer)and/or firmware, or may be implemented using analog and/or digitalhardware, having sufficient memory, interfaces, and capacity to performthe functions described herein.

Acoustic pressure sensors 15-18 sense acoustic pressure signals that, asmeasured, are lower frequency (and longer wavelength) signals than thoseused for ultrasonic flow meters of the prior art, and thus the currentinvention is more tolerant to inhomogeneities in the flow, such asroping and other time and space domain inhomogeneities within the flow,even where entrenchment or coal “roping” is unlikely such as following abend. The term “roping” is a term known to those skilled in this artwhich represents a form of severe spatial and temporal mal-distributioninduced in mixture flows of widely different component densities. It isa condition where a large portion of the coal flow is in a band runningalong one side of pipe 14.

In addition, the present invention incorporates the compliance of thepipe 14 to determine the effective speed of sound of the pipe/PF/airmixture system. The acoustic pressure signals P_(l)(t)−P_(N)(t) aregenerated within the PF/air mixture of the pipe 14 by a variety ofnon-discrete sources such as remote machinery, mills, fans 4 (FIG. 2),valves, elbows, as well as the PF/air mixture flow itself. It is thislast source, the PF/air mixture 12 flowing within the pipe 14, which isa generic source of acoustic noise that assures a minimum level ofacoustics for any PF/air mixture piping systems for which the presentinvention takes unique advantage. The flow generated acoustics increasewith mean flow velocity and the overall noise levels (acoustic pressurelevels) are a function of the generating mechanism and the dampingmechanism. As such, no external discrete noise source is required withinthe present invention and thus may operate using passive listening.While the flow meter 10 passively listens to the mixture flow 12, thepresent invention contemplates adding an acoustic source to inject adesire acoustic wave into the flow to be measured, such as bycompressing, vibrating and/or tapping the pipe, to name a few examples.

For certain types of pressure sensors, e.g., pipe strain sensors,accelerometers, velocity sensors or displacement sensors, discussedhereinafter, it may be desirable for the pipe 14 to exhibit a certainamount of pipe compliance.

Alternatively, to minimize any error effects (and the need for thecorresponding calibration) caused by pipe compliance, the axial testsection 50 of the pipe 14 along where the sensors 15-18 are located maybe made as rigid as possible. To achieve the desired rigidity, thethickness of the wall of the test section 50 may be made to have apredetermined thickness, or the test section 50 may be made of a veryrigid material, e.g., steel, titanium, Kevlar®, ceramic, or othermaterial with a high modulus.

The length of the array (aperture) ΔX of the pressure sensors (15-18) isat least a significant fraction of the measured wavelength of theacoustic waves being measured. As will be described in greater detail,the acoustic wavelength to be measured is a function of at least thedispersion characteristics of the mixture 12, wherein the dispersioncharacteristic is a function of at least the size and mass of theparticles, and the viscosity of the fluid. The greater the dispersion ofthe mixture (e.g. the greater the size and mass, and/or the less viscousthe fluid), the longer the length of the array is needed. Conversely,the lesser the dispersion of the mixture (e.g. the lesser the size andmass, and/or the more viscous the fluid), the shorter the length of thearray is needed.

Further, it is within the scope of the present that the spacing of thepressure sensors may be known or arbitrary, provided the location of thesensors is known. The sensors 15-18 may also be equi-spaced (as shown inFIG. 1) or any non-even or non equi-spaced location, as will bedescribed in greater detail hereinafter. One will appreciate that as fewas two sensors are required if certain information is known about theacoustic properties of the PF/air mixture piping system.

As discussed, the flow meter 10 measures the speed of sound ofone-dimensional sound waves propagating through the fluid/particlemixture to determine the composition of the mixture. Specifically, thespeed of sound propagating through dilute solid/air mixtures can bedirectly related to the mass fraction particles of the flow. A typicalPF fuel delivery system 1 may operate with an air to coal mass ratio of1.5 to 2.5 with coal density of 1200 to 1400 kg/m³ compared to 1.2 kg/m³for air at standard atmospheric conditions. Thus, meeting the desiredmass ratio results in a very dilute mixture of coal on a volumetricbasis, on the order of one part in 1000 by volume.

Assuming that the particles of coal are small enough and the acousticfrequencies and the frequencies of perturbations associated with theacoustics are low enough for the solid particles to exhibit negligibleslip (both steady and unsteady), the sound speed can be assumed to benon-dispersive (that is constant with frequency) and the volumetricphase fraction of the mixture could be determined through the Woodequation:

$\begin{matrix}{\rho_{mix} = {\sum\limits_{i = 1}^{N}\;{\phi_{i}\rho_{i}}}} \\{\frac{1}{\rho_{mix}a_{mix}^{2}} = {\sum\limits_{i = 1}^{N}\frac{\;\phi_{i}}{\rho_{i}a_{i}^{2}}}} \\{{\sum\limits_{i = 1}^{N}\;\phi_{i}} = 1}\end{matrix}$

Including the effect of the compliance introduced by the conduit 12 (inthis case a circular pipe of modulus E, radius R and wall thickness t)

$\frac{1}{\rho_{mix}a_{measured}^{2}} = {{\frac{1}{\rho_{mix}a_{mix}^{2}} + {\sigma\mspace{14mu}{where}\mspace{14mu}\sigma}} \equiv \frac{2R}{Et}}$

Utilizing the relations above, the speed at which sound travels withinthe piping system of a representative coal/air mixtures is shown in FIG.4 as a function of air/coal mass ratio. For this example, the pure airwas assumed to have a density of 1.2 kg/m^3 and a sound speed of 365.9m/s and the coal was assumed to have a density of 1400 kg/m^3 and asound speed of 2439 m/s. As shown, the effect of increasing coalfraction, i.e. decreasing air/coal ratio is to decrease the sound speed.Physically, adding coal particles effectively mass loads the mixture,while not appreciably changing the compressibility of the air. Over theparameter range of interest, the relation between mixture sound speedand air/coal ratio is well behaved and monatomic.

While the calibration curves based on predictions from first principlesare encouraging, using empirical data mapping from sound speed toair/coal ratio may result in improved accuracy of the present inventionto measure the air/coal fractions of the mixture.

However, it has been discovered that the physical properties ofpulverized coal/air mixtures are generally such that there will bevelocity slip at all but very low frequencies (on the order of <1-2 Hzfor nominally 50 μm coal particles in air), as shown in FIGS. 7 and 8which will described in greater detail hereinafter.

FIG. 5 shows the measured speed of sound as a function of frequency foran actual coal/air mixture 12. The sound speed was measured utilizingpassive listening techniques of the present invention as describedherein. The frequency dependence of the sound speed was determined byapplying a Capon array-processing algorithm at multiple narrow frequencyranges between 50-300 Hz thereby determining a frequency specificacoustic propagation velocity. In this particular example, the data wasobtained wherein the coal/air mixture was flowing at nominally 100ft/sec with an air-to-coal mass ratio equal to 1.8. The coal particleswere nominally 50 μm in size, representative of pulverized coaltypically used in power generation and other industrial applications. Amagnified view of the coal particles that were used for this test isshown in FIG. 3.

Further shown in FIG. 5, the sound speed increases with increasingfrequency and asymptotes toward a constant value. The sound speedasymptote at higher frequencies is essentially the sound speedpropagating through air only with no influence of the suspendedparticles. Also, it is apparent that the sound speed of the coal/airmixture has not reached the quasi-steady limit at the lowest frequencyfor which sound speed was measured. The sound speed is continuing todecrease at the lower frequency limit. An important discovery of thepresent invention is that the speed at which sound propagates throughdilute particles suspended in a continuous fluid is said to bedispersive. As defined herein, the speed at which acoustic wavespropagate through dispersive mixtures varies with frequency.

Measuring the sound speed of a mixture 12 at progressively lower andlower frequencies becomes inherently less accurate as the total lengthof the array of pressure sensors 15-18 (Δx_(operature)), which definethe aperature of the array, becomes small compared to the wavelength ofthe acoustics. In general, the aperture should be at least a significantfraction of a wavelength of the sound speed of interest. In a particularembodiment sound speed data was recorded with an array of four sensors,spaced at twelve inches, for a total aperture of three feet. At 50Hz, a1000 ft/sec sound wave has a wavelength of 20 ft. Thus, the aperture ofthis particular array (approx. thirty-six inches) spanned only 3/20thsof a wavelength, and the array's ability to accurately resolve soundspeeds below this was clearly impaired. It is an important aspect of thepresent invention that the ability to resolve sound speed at lowfrequencies is directly related to aperture of the may. Consequentlylonger arrays are used to resolve sound speeds at lower frequencies. Asshown in FIG. 6, the standard deviation associated with determining thespeed of sound in air is shown as a function of frcquency for threearrays of varying aperture, namely 1.5 ft. 3 ft and 10 ft.

Given the practical constraints in accurately measuring sound speeds atultra-low frequencies, the data suggests that utilizing a quasi-steadymodel to interpret the relationship between sound speed, measured atfrequencies above those at which the quasi-steady model is applicable,and the air-to-fuel ratio would be problematic, and may, in fact, beimpractical. Thus, the key to understanding and interpreting thecomposition of coal/air mixtures through sound speed measurements liesin the dispersive characteristics of the coal/air mixture.

In accordance with the present invention the dispersive nature of thesystem utilizes a first principles model of the interaction between theair and particles. This model is viewed as being representative of aclass of models that seek to account for dispersive effects. Othermodels could be used to account for dispersive effects without alteringthe intent of this disclosure (for example, see the paper titled“Viscous Attenuation of Acoustic Waves in Suspensions” by R. L. Gibson,Jr. and M. N. Toksöz), which is incorporated herein by reference. Themodel allows for slip between the local velocity of the continuous fluidphase and that of the particles. The drag force on the particles by thecontinuous fluid is modeled by a force proportional to the differencebetween the local fluid velocity and that of the fluid particles and isbalanced by inertial force:

$F_{drag} = {{K\left( {U_{f} - U_{p}} \right)} = {\rho_{p}v_{p}\frac{\partial U_{p}}{\partial t}}}$where K=proportionality constant, U_(f)=fluid velocity, U_(p)=particlevelocity, ρ_(p)=particle density and v_(p)=particle volume.

The effect of the force on the continuous fluid phase by the fluidparticles is modeled as a force term in the axial momentum equation. Theaxial momentum equation for a control volume of area A and length Δx isgiven by:

${P_{x} - P_{x + {\Delta\; x}} - {{K\left( {U_{f} - U_{p}} \right)}\left\{ \frac{\phi_{p}\Delta\; x}{v_{p}} \right\}}} = {\frac{\partial\;}{\partial t}\left( {\rho_{f}U_{f}\Delta\; x} \right)}$where P=pressure at locations x and Δx, φ_(p)=volume fraction of theparticles, ρ_(f)=fluid density.

The particle drag force is given by:

$F_{drag} = {{K\left( {U_{f} - U_{p}} \right)} = {C_{d}A_{p}\frac{1}{2}{\rho_{f}\left( {U_{f} - U_{p}} \right)}^{2}}}$where C_(d)=drag coefficient, A_(p)=frontal area of particle andρ_(f)=fluid density.

Using Stokes law for drag on a sphere at low Reynold's number gives thedrag coefficient as:

$C_{d} = {\frac{24}{Re} = \frac{24\mspace{11mu}\mu}{{\rho_{f}\left( {U_{f} - U_{p}} \right)}D_{p}}}$where D_(p)=particle diameter and μ=fluid viscosity.

Solving for K in this model yields:K=3πμD _(p)

Using the above relations and 1-dimensional acoustic modelingtechniques, the following relation can be derived for the dispersivebehavior of an idealized fluid particle mixture.

${a_{mix}(\omega)} = {a_{f}\sqrt{\frac{1}{1 + \frac{\varphi_{p}\rho_{p}}{\rho_{f}\left( {1 + {\omega^{2}\frac{\rho_{p}^{2}v_{p}^{2}}{K^{2}}}} \right)}}}}$

In the above relation, the fluid SOS, density (ρ) and viscosity (φ) arethose of the pure phase fluid, v_(p) is the volume of individualparticles and φ_(p) is the volumetric phase fraction of the particles inthe mixture.

Two parameters of primary interest in pulverized coal measurements areparticle size and air-to-fuel mass ratio. To this end, it is of interestto examine the dispersive characteristics of the mixture as a functionof these two variables. FIGS. 7 and 8 show the dispersive behavior forcoal/air mixtures with parameters typical of those used in pulverizedcoal deliver systems.

In particular FIG. 7 shows the predicted behavior for nominally 50 μmsize coal in air for a range of air-to-fuel ratios. As shown, the effectof air-to-fuel ratio is well defined in the low frequency limit.However, the effect of the air-to-fuel ratio becomes indistinguishableat higher frequencies, approaching the sound speed of the pure air athigh frequencies (above ˜100 Hz).

Similarly, FIG. 8 shows the predicted behavior for a coal/air mixturewith an air-to-fuel ratio of 1.8 with varying particle size. This figureillustrates that particle size has no influence on either the lowfrequency limit (quasi-steady) sound speed, or on the high frequencylimit of the sound speed. However, particle size does have a pronouncedeffect in the transition region.

FIGS. 7 and 8 illustrate an important aspect of the present invention.Namely, that the dispersive properties of dilute mixtures of particlessuspended in a continuous fluid can be broadly classified into threefrequency regimes: low frequency range, high frequency range and atransitional frequency range. As best shown in FIG. 8, the speed ofsound propagating through the mixture is substantially the sameregardless of the particle size in the low frequency range. In the lowfrequency range the mixture exhibits a quasi-steady model or a no slip(non-dispersive) characteristic. As shown in the intermediate frequencyrange, the speed of sound propagating through the mixture is dependenton the size of the particle, and thus exhibits dispersivecharacteristics. For the high frequency range, the speed of soundpropagating through the mixture is unaffected by the particles. In otherwords, the speed of sound in the higher frequency range propagatingthrough the mixture is substantially equally to the speed of soundpropagating through the just the fluid with the particles having foreffect, which will be described in greater detail hereinafter.

Knowing the effect of dispersion on the speed of sound through a mixtureas described herein before, one will appreciate that to determine theconcentration of the mixture (e.g., air/fuel ratio), the frequency ofthe measured acoustic wave is within the low frequency range thatexhibits little or no slip (non-dispersive/quasi-steady state), as bestshown in FIG. 7. Further, one will appreciate that to determine theparticle size within the mixture 12, the frequency of the measuredacoustic wave is within the intermediate frequency range that exhibitsdispersive characteristics, as shown in FIG. 8.

Although the effect of particle size and air-to-fuel ratio areinter-related, the predominant effect of air-to-fuel ratio is todetermine the low frequency limit of the sound speed to be measured andthe predominate effect of particle size is to determine the frequencyrange of the transitional regions. As particle size increases, thefrequency at which the dispersive properties appear decreases. Fortypical pulverized coal applications, this transitional region begins atfairly low frequencies, ˜2 Hz for 50 μm size particles.

In the low frequency regime, the particles exhibit negligible slip withthe fluid. The frequency range for which the no-slip, quasi-steadyapproximation is valid is a function of a variety of parametersincluding particle size, continuous phase viscosity, particle shape andparticle density.

The quasi-steady (no-slip condition) sound speed is given by the lowfrequency limit of the above relation, where AFR is air/fuel ratio:

${a_{mix}\left( \omega\rightarrow 0 \right)} = {{a_{f}*\sqrt{\frac{1}{1 + \frac{\varphi_{p}\rho_{p}}{\rho_{f}}}}} \cong {a_{f}*\sqrt{\frac{1}{1 + \frac{1}{AFR}}}}}$Note that particle size does not affect the low frequency limit of thesound speed. Referring to FIG. 9, the sound speed was measured using anembodiment of the present invention having eight sensors at 20.5 inchspacing, averaged from 20-40 Hz, for a range of air-to-coal mass ratios.The sound speed predicted for the coal/air mixtures using thequasi-steady model are also presented. As shown, although the generaltrend is captured, i.e. sound speed decreases with increased coalloading, the error is significant, rendering a first principleinterpretation, based on a quasi-steady model inadequate.

In the high frequency limit, the dispersion relation predicts the soundspeed with asymptote towards the sound speed of the pure fluid.a _(mix)(ω==>∞)=a _(fluid)Interestingly, the high frequency limit is independent of both particlesize and air-to-fuel ratio.

Given the difficulties measuring sufficiently low frequencies to applythe quasi-steady model and recognizing that the high frequency soundspeed contains no direct information on either particle size orair-to-fuel ratio, it becomes apparent that the dispersivecharacteristics of the coal/air mixture should be utilized to determineparticle size and air-to-fuel ratio based on speed of soundmeasurements.

As described hereinbefore, the flow meter 10 of the present inventionincludes the ability to accurately determine the average particle sizeof the coal in the PF/air mixture within the pipe 14 and the air to fuelratio. Provided there is no appreciable slip between the air and thesolid coal particle, the propagation of one dimensional sound wavethrough multiphase mixtures is influenced by the effective mass and theeffective compressibility of the mixture. For an air transport system,the degree to which the no-slip assumption applies is a strong functionof particle size and frequency. In the limit of small particles and lowfrequency, the no-slip assumption is valid. As the size of the particlesincreases and the frequency of the sound waves increase, the non-slipassumption becomes increasing less valid. For a given average coalparticle size, the increase in slip with frequency causes dispersion,or, in other words, the sound speed of the mixture to change withfrequency. With appropriate calibration the dispersive characteristic ofa mixture will provide a measurement of the average particle size, aswell as, the air to fuel ratio (particle/fluid ratio) of the mixture.

Using the model described above, which yields the equation shown below,and experimentally determined sound speed as function of frequency, thepresent invention includes an optimization procedure to simultaneouslydetermine particles size and AFR in coal/air mixtures:

${a_{mix}(\omega)} = {a_{f}\sqrt{\frac{1}{1 + \frac{\varphi_{p}\rho_{p}}{\rho_{f}\left( {1 + {\omega^{2}\frac{\rho_{p}^{2}v_{p}^{2}}{K^{2}}}} \right)}}}}$Referring to FIG. 10 there is shown an optimization procedure inaccordance with the present invention in which the free parameters of ananalytical model are optimized to minimize an error function. Forillustration purposes, the error function utilized is the sum of thedifferences of the sound speeds between an analytical model and theexperimentally determined sound speed as a function of frequency:

${err} = {\sum\limits_{f = f_{low}}^{f = f_{high}}\left( {{a(f)}_{model} - {a(f)}_{measured}} \right)^{2}}$The results of the optimization procedure applied to data recorded froman array of sensors listening to flow in a six inch circular duct, 50 μmparticle size, 100 ft/sec air flow rate with an air-to-fuel ratio of 1.8is shown in FIG. 11. The measured and optimized-model-predicted soundspeed is shown. As shown, the model captures the transitional frequencyrange well and provides a good estimate of the air-to-fuel ratio.

The results of the optimization procedure applied to a series of datasets with varying air-to-fuel ratio is shown in FIG. 12. Note for thisoptimization the particle size was held constant over the range of datasets.

As suggested herein before, the length of the array of pressure sensorsshould be at least a significant fraction of a wavelength of the soundspeed of interest. The significant fraction of the wavelength may be atleast thirty percent of the wavelength, however, this fraction may beless than thirty percent depending on the desired accuracy of themeasurement, the measured wavelength and/or the strength of the acousticwave (e.g., low signal/noise ratio). Therefore, the length of the arrayis dependent on the frequency of the sound speed of interest (frequencybeing inversely proportional to wavelength), wherein the frequency ofthe sound speed of interest is dependent on the measurement to bedetermined (e.g., air/particle ratio and particle size) and thedispersion characteristics of the mixture. For example, the lowfrequency range of the plot of the speed of sound (quasi-steady state)for measuring the concentration of the mixture (e.g., air/particleratio), shown in FIG. 7, is lower as dispersion of the mixtureincreases. As described herein before, the dispersion characteristics ofthe mixture is dependent on the size of the particles among otherfactors. As the particle size increases, the dispersion becomes greater,and as the particle size decreases, the dispersion becomes lower.Consequently, the length of the array is a function of the size of theparticle within the mixture, and therefore, as best shown in FIG. 8, thetransition point (low frequency cut-off) between the low frequency rangeand the intermediate frequency decreases in frequency as the particlesize increases.

For example when measuring the concentration of the mixture, as the sizeof the particles increase, the low frequency cut-off decreases and thus,the acoustic wavelength of interest increases to thereby necessitate thelength of the array to be longer. Conversely, as the size of theparticles decrease, the low frequency cut-off increase and thus, theacoustic wavelength of interest decreases to thereby necessitate thelength of the array to be shorter. Simply stated, the larger theparticle, the longer the array and vice versa. The same comparison istrue when determining the size of the particles within the mixture.However, for optimal performance of the flow meter, the measurement ofthe concentration of the mixture may require a longer array than themeasurement of the particle size because measurement of theconcentration is at a lower frequency (longer wavelength) than theintermediate frequency (shorter wavelength) of the particle size.

The lowest practical measurable frequency range is approximately 10-25Hz, therefore the measurement of large particle may not be possible tomeasure the quasi-steady model, which may in some instances be less than10 Hz (i.e., cut-off frequency less than 10 Hz). Under thesecircumstances, the frequency of the speed of sound of interest is abovethe cut-off frequency. However, the measured speed of sound is curve fitto a dispersion model of the mixture by varying the size of the particleand the composition of the mixture to determine the particle size and/orconcentration of the mixture, as shown in FIG. 10 that will be describedin greater detail hereinafter.

While the length of the array is dependent on the particle size, thelength may also be dependent on other parameters that define the amountof dispersion, such as mass of the particles and the viscosity of thefluid within the mixture.

Another factor that defines (or effects) the length of the array ofpressure sensors 15-18 includes the signal strength of the acoustic wavereceived by the processor. As the signal strength improves or isgreater, the shorter the length of the array must be. The signalstrength is dependent on a number of factors, such as the strength ofthe acoustic wave itself, the signal/noise ratio of the sensors, thematching of the sensors and others.

The spacing may be equi-spaced as shown in FIG. 1, however the flowmeter 10 of the present invention contemplates that the sensors may havenon-equal or uneven spacing therebetween. The sensors may be spaced anydesired distance, provided the location or position of the sensors areknown. For ported pressure sensors, the minimum spacing is limited bymechanical limitations of the sensors. For strain-based sensors, such asPVDF bands described hereinafter, the compliance of the pipe limits thecloseness of the spacings. For example, the more rigid the pipe, thegreater the spacing of the sensors must be, and conversely, the morecompliant the pipe, the closer the sensors may be spaced.

The spacing of the pressure sensors may also be defined by the number ofsensors disposed within an array of a given length. The more sensorsdisposed within the array of a given length, the closer the spacing. Thenumber of sensors disposed within an array is dependent on the requiredor desired accuracy of the flow meter 10. The greater the number ofsensors in the array, a more precise measurement of the acousticpressure field can be achieved. In other words, a greater number ofsamples or measurements of the acoustic pressure wave over a givenlength of the array (or wavelength) provided the sensors enable greaterresolution in the measurement of the acoustic wave to be measured orcharacterized.

In addition to measuring the fluid to particle ratio of the mixture 12and particle size within a pipe 14 using the measured speed of sound,the flow meter 10 further includes the ability to measure of volumetricflow rate of the mixture by comparing the difference of the speed of onedimensional sound waves propagating with and against the mean flow.

This method of determining the volumetric flow rate of theparticle/fluid mixture 12 within pipe 14 relies on the interaction ofthe mean flow with the acoustic pressure field. The interaction resultsin sound waves propagating with the mean flow traveling at the speed ofsound (if the particle/liquid mixture were not flowing) plus theconvection velocity and, conversely, sound waves traveling against themean flow propagating at the speed of sound minus the convectionvelocity. That is,a _(R) =a _(mix) +ua _(L) =a _(mix) −uwhere a_(R)=velocity of a right traveling acoustic wave relative to astationary observer (i.e. the pipe 14), a_(L)=velocity of a lefttraveling acoustic wave apparent to a stationary observer, a_(mix)=fluidspeed of sound (if the fluid were not flowing) and u=the mean flowvelocity (assumed to be flowing from left to right in this instance).Combining these two equations yields an equation for the mean velocity,

$u = \frac{a_{R} - a_{L}}{2}$Therefore, by measuring the propagation velocity of acoustic waves inboth directions relative to the stationary pipe as describedhereinbefore, the mean flow velocity can be calculated by multiplyingthe mean flow velocity by the cross-sectional area of the pipe 14.

The practicality of using this method to detemilne the mean flow ispredicated on the ability to resolve the sound speed in both directionswith sufficient accuracy to determine the volumetric flow. For typicalliquid measurements, flow velocities are typically at ˜10 ft/sec andsound speeds of ˜4000 ft/sec. Thus axial mach numbers are on the orderof 10/4000 of 0.0025. For a +/−10% accuracy in flow rate (+/−7ft/sec),the sound speed of the upstream and downstream propagating waves wouldneed to be resolved to +/−0.5/4000 or one part in 8,000.

However, for PF/air mixture flows, axial flow velocities are nominallyaround 70 ft/sec with no flow sound speeds of ˜700 ft/sec. This resultsin mach numbers of ˜0.1, approximately two orders of magnitude greaterthan typical liquid flows For pulverized fuel flows, to resolve the flowrate to 10% accuracy (or +/−7 ft/sec), one would have to resolve thesound speed to +/−3.5 ft/sec. or 3.5/700 or one part in 200.

For the sound speed measurement, the flow meter 10 utilizes similarprocessing algorithms as those employed herein before. The temporal andspatial frequency content of sound propagating within the process piping14 is related through a dispersion relationship.ω=kα _(mix)The wave number is k, which is defined as k=2π/λ, ω is the temporalfrequency in rad/sec, and a_(mix) is the speed at which sound propagateswithin the process piping. For this cases where sound propagates in bothdirections, the acoustic power is located along two acoustic ridges, onefor the sound traveling with the flow at a speed of a_(mix)+V_(mix) andone for the sound traveling against the flow at a speed ofa_(mix)−V_(mix).

The k-w plot shown in FIG. 13 illustrates the fundamental principlebehind sonar based flow measure, namely that axial arrays of pressuresensors can be used in conjunction with sonar processing techniques todetermine the speed at which naturally occurring turbulent eddiesconvect within a pipe. FIG. 13 shows a k-ω plot generated for acousticsound field of a coal/air mixture flowing through a pipe. Two acousticridges are clearly evident. Each of the slopes of the two depictedacoustic ridges respectively defines the speed of sound traveling withand against the mean flow, respectively. A parametric optimizationmethod was used to determine the “best” line representing the slope ofthe acoustic ridge.

Further, FIG. 13 illustrates the ability of the present invention todetermine the velocity of a fluid moving in a pipe. FIG. 13 shows awavenumber-frequeney plot (k-w plot) of unsteady pressure. The contoursrepresent the relative signal power at all combinations of frequency andwavenumber. The highest power “ridges” represent the acoustic wave withslope of the ridges equal to the propagation speed. The dashed linesshow the best-fit two-variable maximization of the power with the twovariables being sound speed and flow velocity. The right-side ridgerepresents the acoustic wave traveling in the same direction as the bulkflow and therefore its slope is steeper than the left-side ridge thatrepresents the acoustic wave traveling in the opposite direction of thebulk flow. This indicates that the acoustic wave traveling in the samedirection of the flow is traveling faster than the acoustic wavetraveling in the opposite direction of the bulk flow relative to thestationary sensors located on the pipe.

The pressure sensors 15-18 described herein may be any type of pressuresensor, capable of measuring the unsteady (or ac or dynamic) pressureswithin a pipe 14, such as piezoelectric, optical, capacitive, resistive(e.g., Wheatstone bridge), accelerometers (or geophones), velocitymeasuring devices, displacement measuring devices, etc. If opticalpressure sensors are used, the sensors 15-18 may be Bragg grating basedpressure sensors, such as that described in U.S. patent application Ser.No. 08/925,598, entitled “High Sensitivity Fiber Optic Pressure SensorFor Use In Harsh Environments”, filed Sep. 8, 1997, now U.S. Pat. No.6,016,702. Alternatively, the sensors 14 may be electrical or opticalstrain gages attached to or embedded in the outer or inner wall of thepipe which measure pipe wall strain, including microphones, hydrophones,or any other sensor capable of measuring the unsteady pressures withinthe pipe 14. In an embodiment of the present invention that utilizesfiber optics as the pressure sensors 14 they may be connectedindividually or may be multiplexed along one or more optical fibersusing wavelength division multiplexing (WDM), time division multiplexing(TDM), or any other optical multiplexing techniques.

For any of the embodiments described herein, the pressure sensors,including electrical strain gages, optical fibers and/or gratings amongothers as described herein, may be attached to the pipe by adhesive,glue, epoxy, tape or other suitable attachment means to ensure suitablecontact between the sensor and the pipe 14. The sensors mayalternatively be removable or permanently attached via known mechanicaltechniques such as mechanical fastener, spring loaded, clamped, clamshell arrangement, strapping or other equivalents. Alternatively, thestrain gages, including optical fibers and/or gratings, may be embeddedin a composite pipe. If desired, for certain applications, the gratingsmay be detached from (or strain or acoustically isolated from) the pipe14 if desired.

It is also within the scope of the present invention that any otherstrain sensing technique may be used to measure the variations in strainin the pipe, such as highly sensitive piezoelectric, electronic orelectric, strain gages attached to or embedded in the pipe 14.

In certain embodiments of the present invention, a piezo-electronicpressure transducer may be used as one or more of the pressure sensors15-18 and it may measure the unsteady (or dynamic or ac) pressurevariations inside the pipe 14 by measuring the pressure levels inside ofthe pipe. In an embodiment of the present invention, the sensors 14comprise pressure sensors manufactured by PCB Piezotronics. In onepressure sensor there are integrated circuit piezoelectric voltagemode-type sensors that feature built-in microelectronic amplifiers, andconvert the high-impedance charge into a low-impedance voltage output.Specifically, a Model 106B manufactured by PCB Piezotronics is usedwhich is a high sensitivity, acceleration compensated integrated circuitpiezoelectric quartz pressure sensor suitable for measuring low pressureacoustic phenomena in hydraulic and pneumatic systems. It has the uniquecapability to measure small pressure changes of less than 0.001 psiunder high static conditions. The 106B has a 300 mV/psi sensitivity anda resolution of 91 dB (0.0001 psi).

The pressure sensors incorporate a built-in MOSFET microelectronicamplifier to convert the high-impedance charge output into alow-impedance voltage signal. The sensor is powered from aconstant-current source and can operate over long coaxial or ribboncable without signal degradation. The low-impedance voltage signal isnot affected by triboelectric cable noise or insulationresistance-degrading contaminants. Power to operate integrated circuitpiezoelectric sensors generally takes the form of a low-cost, 24 to 27VDC, 2 to 20 mA constant-current supply. A data acquisition system ofthe present invention may incorporate constant-current power fordirectly powering integrated circuit piezoelectric sensors.

Most piezoelectric pressure sensors are constructed with eithercompression mode quartz crystals preloaded in a rigid housing, orunconstrained tourmaline crystals. These designs give the sensorsmicrosecond response times and resonant frequencies in the hundreds ofkHz, with minimal overshoot or ringing. Small diaphragm diameters ensurespatial resolution of narrow shock waves.

The output characteristic of piezoelectric pressure sensor systems isthat of an AC-coupled system, where repetitive signals decay until thereis an equal area above and below the original base line. As magnitudelevels of the monitored event fluctuate, the output remains stabilizedaround the base line with the positive and negative areas of the curveremaining equal.

Furthermore the present invention contemplates tat each of the pressuresensors 15-18 of the flow meters 10,70 may include a piezoelectricsensor 104-107 that provides a piezoelectric material 110 to measure theunsteady pressures of the fluid/particle mixture 12 as shown in FIG. 14.The piezoelectric material, such as the polymer, polarizedfluoropolymer, polyvinylidene fluoride (PVDF), measures the straininduced within the process pipe 14 due to unsteady pressure variationswithin the process mixture 12. Strain within the pipe is transduced toan output voltage or current by the attached piezoelectric sensors104-107.

As best shown in FIG. 15, the PVDF material 110 is adhered to the outersurface of a steel strap 112 that extends around and clamps onto theouter surface of the pipe 14. The piezoelectric sensing element istypically confonnal to allow complete or nearly complete circumferentialmeasurement of induced strain to provide a circumference-averagedpressure. The sensors can be formed from PVDP films, co-polymer films,or flexible PZT sensors, similar to that described in “Piezo FilmSensors technical Manual” provided by Measurement Specialties, Inc.,which is incorporated herein by reference. The advantages of thistechnique are the following:

-   -   1. Non-intrusive flow rate measurements    -   2. Low cost    -   3. Measurement technique requires no excitation source. Ambient        flow noise is used as a source.    -   4. Flexible piezoelectric sensors can be mounted in a variety of        configurations to enhance signal detection schemes. These        configurations include a) co-located sensors, b) segmented        sensors with opposing polarity configurations, c) wide sensors        to enhance acoustic signal detection and minimize vortical noise        detection, d) tailored sensor geometries to minimize sensitivity        to pipe modes, e) differencing of sensors to eliminate acoustic        noise from vortical signals.    -   5. Higher Temperatures (140C.) (co-polymers)

While the present invention illustrates that the array of pressuresensors comprises a plurality of like sensors, the present inventioncontemplates that any combination of different or similar pressuresensors may be used within an array.

While the present invention is capable of measuring solid particlessuspended in a fluid, one will appreciate that other multi-phasemixtures or flows may be measured using an array of sensors, such assteam flow. It is further recognize the that effects of dispersion onlarge solid particles in a fluid would be similar to large droplets of aliquid dispersed in a gas or air, and thus similar considerations whenmeasuring the steam quality and droplet size should be addressed.

It should be understood that any of the features, characteristics,alternatives or modifications described regarding a particularembodiment herein may also be applied, used, or incorporated with anyother embodiment described herein.

Although the invention has been described and illustrated with respectto exemplary embodiments thereof, the foregoing and various otheradditions and omissions may be made therein and thereto withoutdeparting from the spirit and scope of the present invention.

1. An apparatus for measuring at least one parameter of a dispersivemixture of solids and fluid flowing in a pipe, said apparatuscomprising: a spatial array of pressure sensors, disposed at differentaxial locations along the pipe, to measure an pressure within the pipeat each corresponding axial location, each of said sensors providing apressure signal indicative of the pressure within the pipe at saidcorresponding axial location; and a signal processor, responsive to saidpressure signals, to determine the speed of sound propagating throughthe dispersive mixture as a function of frequency at multiplefrequencies and to use the speed of sound and a dispersion model of thedispersive mixture to provide output corresponding to at least oneparameter of the dispersive mixture flowing in the pipe.
 2. Theapparatus of claim 1, wherein each sensor measures an acoustic pressureand provides a signal indicative of an acoustic noise within the pipe.3. The apparatus of claim 1, wherein the signal processor, responsive tosaid pressure signals, outputs the speed of sound propagating throughthe mixture in the pipe.
 4. The apparatus of claim 3, wherein saidsignal processor comprises logic which calculates a speed at which soundpropagates axially past said spatial array.
 5. The apparatus of claim 4,wherein said pressure signals each comprise a frequency based signal andwherein said signal processor comprises logic which calculates a ratioof two of said frequency based signals.
 6. The apparatus of claim 3,wherein said signal processor comprises logic which calculates afrequency based signal for each of said pressure signals.
 7. Theapparatus of claim 3, wherein the signal processor comprises logic whichcalculates a fluid composition of the mixture in the pipe.
 8. Theapparatus of claim 3, wherein the array of pressure sensors are spacedsufficiently such that the entire length of the array is at least asignificant fraction of a measured wavelength of acoustic waves beingmeasured.
 9. The apparatus of claim 1, comprising at least three of saidsensors.
 10. The apparatus of claim 1, wherein at least one of saidpressure sensors measures a circumferential pressure at said axiallocation of said sensor.
 11. The apparatus of claim 10 wherein at leastone of said pressure sensors includes a piezoelectric film material. 12.The apparatus of claim 11, wherein the piezoelectric film material ispolarized fluoropolymer, polyvinylidene fluoride (PVDF).
 13. Theapparatus of claim 1, wherein each of said pressure sensors is a strainsensor that measures strain on the pipe.
 14. The apparatus of claim 1,wherein the signal processor uses the speed of sound propagating throughthe mixture to characterize dispersion properties of the mixture andcompares the dispersion properties of thc mixture to a dispersion modelof the mixture to provide a signal indicative of the at least oneparameter of the mixture.
 15. The apparatus of claim 1, wherein thedispersion model is empirically derived.
 16. The apparatus of claim 1,wherein the dispersion model is numerically derived.
 17. The apparatusof claim 16, wherein the numerically derived dispersion model is:${a_{mix}(\omega)} = {a_{f}\sqrt{\frac{1}{1 + \frac{\varphi_{p}\rho_{p}}{\rho_{f}\left( {1 + {\omega^{2}\frac{\rho_{p}^{2}v_{p}^{2}}{K^{2}}}} \right)}}}}$wherein α_(mix)(ω)=speed of sound propagating through the mixture;α_(f)=speed of sound propagating through the fluid; φ_(p)=volumefraction of the particles; ω=frequency; ρ_(p),ρ_(t)=density of particlesand fluid, respectively; υ=volume of a particle; K=proportionalityconstant.
 18. The apparatus of claim 1, wherein the at least oneparameter of the mixture includes at least one of a particle/fluidcomposition, a volumetric phase fraction, a volumetric flow rate,particle size, mass flow, density, velocity of the mixture in the pipe,and a speed of sound propagating through the mixture in the pipe. 19.The apparatus of claim 1, wherein the signal processor furthercharacterizes the dispersion properties of the mixture in response to atleast one of the pressure of the mixture, temperature of the mixture,density of particle phase and density of the fluid phase.
 20. Theapparatus of claim 1, wherein the signal processor compares at least atransitional frequency range of the dispersion model to determine anaverage particle size in the mixture.
 21. The apparatus of claim 1,wherein the signal processor compares at least one of a lower frequencyrange and a transitional frequency range of the dispersion model todetermine a particle/fluid ratio of the mixture.
 22. The apparatus ofclaim 1, wherein the signal processor defines an acoustic ridge in a k-ωplane and determines a slope of the at least a portion of the acousticridge to determine the speed of sound propagating through the mixture.23. The apparatus of claim 1, wherein the sensors include at least oneof pressure sensors and strain-based sensors.
 24. The apparatus of claim1, wherein the unsteady pressure is a passive acoustic wave propagatingaxially through the dispersive mixture flowing in the pipe.
 25. Theapparatus of claim 1, wherein the spatial array includes at least twopressure sensors.
 26. A method for measuring at least one parameter of adispersive mixture of a solid and fluid flowing in a pipe, said methodcomprising: measuring pressures within the pipe at at least two axialmeasurement locations disposed along the pipe to provide correspondingpressure signals indicative of the pressure within the pipe at each ofthe at least two axial measurement locations; determining the at leastone parameter of the dispersive mixture of a solid and fluid flowing inthe pipe using the pressure measured at the axial measurement locationsto determine the speed of sound propagating through the mixture as afunction at multiple frequencies and using the speed of sound and adispersion model of the dispersive mixture, and generating an outputcorresponding to the at least one parameter.
 27. The method of claim 26,wherein the measured pressures are acoustic pressures to provide asignal indicative of an acoustic noise within the pipe.
 28. The methodof claim 27, wherein the determining the at least one parameter uses anacoustic pressure to calculate a speed of sound propagating in the pipe.29. The method of claim 28, wherein a spatial array of sensors measuressaid pressure and the determining the at least one parametcr uses anacoustic pressure to calculate a speed at which sound propagates axiallypast said spatial array.
 30. The method of claim 29, wherein saidacoustic pressure signals each comprise a frequency based signal andwherein said method further includes providing a signal processorcomprising logic which calculates a ratio of two of said frequency basedsignals.
 31. The method of claim 28, wherein the determining the atleast one parameter uses an acoustic pressure to calculate a frequencybased signal for each of said acoustic pressure signals.
 32. The methodof claim 28, wherein the step of determining the at least one parameteruses an acoustic pressure to calculate a fluid composition of themixture in the pipe.
 33. The method of claim 28, further includingproviding an array of pressure sensors, and said step of measuringpressures includes measuring acoustic waves, said array of pressuresensors being spaced sufficiently such that an entire length of thearray is at least a significant fraction of a measured wavelength of theacoustic waves being measured.
 34. The method of claim 26, furthercomprising providing at least three sensors to measure the unsteadypressure.
 35. The method of claim 26, wherein measuring pressureincludes measuring a circumferential pressure at at least an axiallocation of a sensor.
 36. The method of claim 35, wherein said sensorincludes a piezoelectric film material.
 37. The method of claim 36,wherein the piezoeleetric film material is polarized fluorop.olymer,polyvinylidene fluoride (PVDF).
 38. The method of claim 26, wherein thestep of measuring pressures includes providing at least one strainsensor that measures strain on the pipe to provide at least a portion ofthe corresponding pressure signals.
 39. The method of claim 26, whereinsaid determining the at least one parameter uses the speed of soundpropagating through the mixture to characterize dispersion properties ofthe mixture and compares the dispersion properties of the mixture to adispersion model of the mixture to provide a signal indicative of the atleast one parameter of the mixture.
 40. The method of claim 26, whereinthe dispersion model is empirically derived.
 41. The method of claim 26,wherein the dispersion model is numerically derived.
 42. The method ofclaim 41, wherein the numerically derived dispersion model is:${a_{mix}(\omega)} = {a_{f}\sqrt{\frac{1}{1 + \frac{\varphi_{p}\rho_{p}}{\rho_{f}\left( {1 + {\omega^{2}\frac{\rho_{p}^{2}v_{p}^{2}}{K^{2}}}} \right)}}}}$wherein α_(mix)(ω)=speed of sound propagating through the mixture;α_(f)=speed of sound propagating through the fluid; φ_(p)=volumefraction of the particles; ω=frequency; ρ_(p)ρ_(f)=density of particksand fluid, respectively; υ=volume of a particle; K=proportionalityconstant.
 43. The method of claim 26, wherein said solids areparticulate and the at least one paramctcr of the mixture includes atleast one of a particle/fluid composition, a volumetric phase fraction,a volumetric flow rate, particle size, mass flow, density, velocity ofthe mixture in the pipe, and speed of sound propagating through themixture in thc pipe.
 44. The method of claim 26, wherein said step ofdetermining the at least one parameter further characterizes thedispersion properties of the mixture in response to at least one of thepressure of the mixture, temperature of the mixture, density of particlephase and density of the fluid phase.
 45. The method of claim 26,wherein said step of determining the at least one parameter compares atleast an intermediate frequency range of the dispersion model todetermine the average particle size in the mixture.
 46. The method ofclaim 26, wherein said calculating the at least one parameter comparesat least one of a lower frequency range and an intermediate frequencyrange of the dispersion model to determine a particle/fluid ratio of themixture.
 47. The method of claim 26, further includes determining afrequency based signal for each of said pressure signals.
 48. The methodof claim 26, wherein the measuring of unsteady pressures within the pipeis accomplished using at at least one of 3, 4, 5, 6, 7, 8, 9, 10, 11,12, 13, 14, 15 and 16 sensors disposed at respective axial locations.49. The method of claim 26, wherein said step of determining the atleast one parameter defines an acoustic ridge in a k-ωplane anddetermines a slope of at least a portion of a acoustic ridge todetermine the speed of sound propagating through the mixture.
 50. Anapparatus for measuring at least one parameter of a dispersive mixtureof a solid and a fluid flowing in a pipe, said apparatus comprising: asignal processor, responsive to a signal indicative of the speed ofsound propagating through the dispersive mixture of a solid and a fluidflowing within the pipe as a function of frequency at multiplefrequencies, to determine the at least one parameter of the dispersivemixture in the pipc using a dispersion model of the dispersive mixture,said signal processor being configured to produce an outputcorresponding to the at least one parameter.
 51. The apparatus of claim50, wherein the signal processor further characterizes the dispersionproperties of the dispersive mixture and compares the dispersionproperties of the mixture to a dispersion model of thc dispersivemixture to provide a signal indicative of the at least one parameter ofthe mixture.
 52. A method for measuring at least one parameter of adispersive mixture of a solid and a fluid flowing in a pipe, said methodcomprising: receiving a signal indicative of the speed of soundpropagating through the dispersive mixture of a solid and a fluidflowing in a pipe as a function of frequency at multiple frequencies;determining the at least one parameter of the dispersive mixture in thepipe using the signal indicative of the speed of sound at multiplefrequencies and a dispersion model of the dispersive mixture; andproducing an output corresponding to the at least one parameter.
 53. Themethod of claim 52, wherein said determining the at least one parameterfurthet characterizes dispersion properties of the mixture using thesignal indicative of the speed of sound propagating through the mixtureand compares the dispersion properties of the mixture to a dispersionmodel of the mixture to provide a signal indicative of the at least oneparameter of the mixture.